The Dynamics and Interaction of Quantized Vortices in Ginzburg-Landau-Schrodinger Equation

报告摘要：

In this talk, we investigate the dynamical laws of quantized vortex
interaction in the Ginzburg-Lanau-Schrodinger equation (GLSE) analytically
and numerically. We begin with a review of the reduced dynamic laws governing
the motion of vortex centers in GLSE and solve the nonlinear ordinary
differential equations (ODEs) of the reduced dynaqmical laws analytically
with a few types of initial data. By directly simulating the GLSE with an
efficient and accurate numerical method proposed recently by us,
we can compare quantized vortex interaction patterns of GLSE with those from
the reduced dynamic laws qualitatively and quantitatively. Some conclusive
experimental findings are obtained, and discussions on numerical and
theoretical results are made to provide further understanding of vortex
interactions in GLSE. Finally, the vortex motion under an inhomogeneous
potential is also studied.